A consulting firm consists of a number of offices spread out geographically. Each office has a number of employees. Each employee has specialized knowledge.
Teams are formed as needed depending on the particular project. Each team is tasked to produce technical reports which are then delivered to our clients.
Organizationally, the firm consists of office managers and project managers. The office managers are responsible for the employees at their local office. The team reports to project managers. The project manager is responsible for delivering the report to the client.
The firm has problem meeting deadlines. The deliverable dates to the clients are known to all the employees. In practice, the employees interpret these dates as the due date for their individual contribution. The employees ignor earlier dates requested by the project manager. The problem with this is that the reports sometimes need to be re-written, re-organized, reviewed, or whatever. Consequently the reports are delivered either sub-quality or late.
I am looking for techniques to better improve this situation. Does it take a buy in from each of the office managers or are their other techniques to address this issue?
Are their any books that address these types of issues either specifically or in a more general context?

Feedback & project MANAGEMENT
Without more specifics it's hard to give any advice. The question sounds very abstract.
You shouldn't need buy-in. The office managers should know that their people have deadlines to meet, and you need the PMs to give feedback to both the team members and their line managers that deadlines are not being met. Regardless of when a client deliverable is, the individual contributors have deadlines that they are not meeting. This is both their fault and the fault of the PMs, who should own the deliverables.
The PMs need to actually manage their projects (which includes ensuring they are delivered on time), and the line managers (or "office managers") need to ensure their people can meet the necessary deadlines.
Deadlines
I think it is fairly obvious the INDIVIDUAL deadlines need to be adjusted to give the FINAL deadline time for compilation, proofing and amendment.
Ask the individual to nominate their own deadline after the extent task is known and then insist they keep their own individual promise.